OAI/MathematicalPhysics/DefocusingNLS/Certificates/BoundaryDeterminantPositivity.lean

GitHub source file

5 declarations, 0 contain sorry, 0 declared as axioms

Positivity of the coherent raw boundary determinant

  1. theorem OAI.DefocusingNLS.BoundaryCertificate.certificate_first line 14
  2. theorem OAI.DefocusingNLS.BoundaryCertificate.certificate_second line 21
  3. theorem OAI.DefocusingNLS.BoundaryCertificate.certificate_third line 28
  4. theorem OAI.DefocusingNLS.BoundaryCertificate.chart_value_positive line 35
  5. theorem OAI.DefocusingNLS.BoundaryCertificate.rawDeterminant_positive line 59

    Source documentation

    The entire parameter box, including repeated coherent occurrences of b,Z, has strictly positive determinant at every real frequency.

    theorem rawDeterminant_positive (ell : Fin 4) (b Z v : ℝ)
    (hb : |100000000 * b - 33477607| ≤ 2) (hZ : |100000000 * Z - 270506819| ≤ 2) :
    0 < ((rawDeterminant ell b Z).eval (v : ℂ)).re := by
…

    Mentions: OAI.DefocusingNLS.BoundaryCertificate.rawDeterminant